Question: Rewrite as a simplified fraction. ${0.58\overline{1} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 581.1111...\\ 100x &= 58.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 523}$ ${x = \dfrac{523}{900}} $